With the penalty linear in the number of candidate change points as
\(p_n(\mathcal {A}) = (1 + \epsilon )\log (n) \cdot \vert \mathcal {A} \vert \) ,
the consistency of \(\mbox{SC}\)  in estimating the total number of change points has been established
under i.i.d. Gaussianity, in [1]} (with \(\epsilon = 0\) )
and [2]} (with a small constant \(\epsilon > 0\) ),
in the setting where both \(q_n\)  and \(N\)  are fixed with \(N > q_n\) .
This result is complemented by [3]}, where
the consistency of the least squares estimators of \(\theta _j,\)  \(1 \le j \le q_n\) ,
is established and their distribution is derived when \(q_n\)  is fixed and known.
Penalties depending on the spacing between the change points as well as the total number \(\vert \mathcal {A} \vert \) ,
are considered in [4]}, [5]} and [6]},
and the application of the Akaike information criterion to the change point problem
is studied in [7]}.
